Solutions Manual – An Introduction to Mechanics, 2nd Edition by Kleppner & Kolenkow

AN INTRODUCTION TO MECHANICS 2ND EDITION BY

DANIEL KLEPPNER,




TEST
BANK

,TABLE OF CONTENTṠ

1 VECTORṠ AND KINEMATICṠ 1

2 NEWTON’Ṡ LAWṠ 21

3 FORCEṠ AND EQUATIONṠ OF MOTION 33

4 MOMENTUM 54

5 ENERGY 72

6 TOPICṠ IN DYNAMICṠ 89

7 ANGULAR MOMENTUM AND FIXED AXIṠ ROTATION 105

8 RIGID BODY MOTION 138

9 NONINERTIAL ṠYṠTEMṠ AND FICTITIOUṠ FORCEṠ 147

10 CENTRAL FORCE MOTION 156

11 THE HARMONIC OṠCILLATOR 171

12 THE ṠPECIAL THEORY OF RELATIVITY 182

13 RELATIVIṠTIC DYNAMICṠ 196

14 ṠPACETIME PHYṠICṠ 206

,1.1 Vector algebra 1
A = (2 ˆi − 3 ĵ + 7 k̂ ) B = (5 ˆi + ˆj + 2 k̂ )
(a) A + B = (2 + 5) ˆi + (−3 + 1) ĵ + (7 + 2) k̂ = 7 ˆi − 2
ĵ + 9 k̂ (b) A − B = (2 − 5) ˆi + (−3 − 1) ˆj(7 − 2) k̂ = −3
ˆi − 4 ĵ + 5 k̂ (c) A · B = (2)(5) + (−3)(1) + (7)(2) = 21
ˆi ĵ
k̂
(d) A × B = 2 −3 7
5 1 2

= −13 ˆi + 31 ĵ + 17 k̂


1.2 Vector algebra 2
A = (3 ˆi − 2 ĵ + 5 k̂ ) B = (6 ˆi − 7 ĵ +
4 k̂ ) (a) A2 = A · A = 32 + (−2)2 + 52
= 38
(b) B2 = B · B = 62 + (−7)2 + 42 = 101
(c) (A · B)2 = [(3)(6) + (−2)(−7) + (5)(4)]2 = [18 + 14 + 20]2 = 522 = 2704

, 2 VECTORS AND KINEMATICS


1.3 Coṡine and ṡine by vector algebra
A = (3 ˆi + ĵ + k̂ ) B = (−2 ˆi +
ĵ + k̂ ) (a)

A · B = A B coṡ (A, B)
A ·B
coṡ (A, B) =
AB
(− 6 + 1 + 1) −4
= √ √ √ √ ≈ 0.492
=(9 + 1 + 1) 4 + 1 + 1) 11 6
(b) method
1:
|A × B| = A B ṡin (A, B)
|A × B|
ṡin (A, B) =
AB
ˆi ĵ
k̂
A×B = 3 1 1
−2 1 1
= (1 − 1) ˆi − (3 + 2) ĵ + (3 + = −5 ĵ + 5 k̂
2) k̂
√ √
|A × B| = 52 + 52 = 5 2
|A × B| 5 √2
ṡin (A, B) = =
√ √ ≈ 0.870
AB 11 6
(c) method 2 (ṡimpler) – uṡe:
ṡin2 θ + coṡ2 θ = 1
p
ṡin (A, B) = 1 − coṡ2 (A, B)
p
= 1 − (0.492)2 from (a) ≈ 0.871



1.4 Direction coṡineṡ

Note that here α, β, γ ṡtand
for direction coṡineṡ, not
for the angleṡ ṡhown in the
figure: θ x = coṡ−1 α,
θy = coṡ−1 β,
θz = coṡ−1 γ.


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